Questions: 3/4(-8v-4)=2(v+6)-3v

3/4(-8v-4)=2(v+6)-3v
Transcript text: $\frac{3}{4}(-8 v-4)=2(v+6)-3 v$
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Solution

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Solution Steps

To solve the equation \(\frac{3}{4}(-8v - 4) = 2(v + 6) - 3v\), we need to follow these steps:

  1. Distribute the \(\frac{3}{4}\) on the left-hand side.
  2. Simplify both sides of the equation.
  3. Combine like terms.
  4. Solve for \(v\).
Step 1: Distribute and Simplify

First, distribute \(\frac{3}{4}\) on the left-hand side of the equation: \[ \frac{3}{4}(-8v - 4) = -6v - 3 \] The equation becomes: \[ -6v - 3 = 2(v + 6) - 3v \]

Step 2: Simplify the Right-Hand Side

Next, simplify the right-hand side of the equation: \[ 2(v + 6) - 3v = 2v + 12 - 3v = 12 - v \] So the equation now is: \[ -6v - 3 = 12 - v \]

Step 3: Combine Like Terms

Combine like terms to isolate \(v\): \[ -6v + v = 12 + 3 \] \[ -5v = 15 \]

Step 4: Solve for \(v\)

Solve for \(v\) by dividing both sides by \(-5\): \[ v = \frac{15}{-5} = -3 \]

Final Answer

\(\boxed{v = -3}\)

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